#include <cmath>
#include <limits>

const double eps = 4 * std::numeric_limits<double>::epsilon();
const int INF = std::numeric_limits<int>::max();

struct point
{
	double x,y;
	point (double, double);
	point ();
	bool operator != (const point&) const;
	bool operator == (const point&) const;
	bool operator < (const point&) const;
};

bool points_x_predicate(const point&, const point&);
int left_turn (const point&, const point&, const point&);
int left_turn_add_precision(const point&, const point&, const point&);